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Gigabyte GA-H61M-S1 motherboard infinite boot

I have 3 computers with the Gigabyte GA-H61M-S1 rev 2.1 motherboard.
I was using one of them but after restarting it, it got into an infinite boot with no display (integrated GPU there is no internal GPU) and no USB input and there is no POST test, no Gigabyte logo, and no DEL/F9/F12 to enter BIOS. I say an “infinite loop”, not a “boot loop”.

At first, I did think that it was only with this computer, but after testing the 2 others they have the same problem.
Here is what I tried (multiple times):

  • unplug the PSU from the wall plug and pressing the power button for 1 minute + removing the motherboard battery.
  • using a jumper to clear the CMOS.

It doesn’t stop there. Even without understanding how this following miracle happened, one in 10 trials after resetting the BIOS and after 10-15 minutes of black screen, the screen finally displayed something which is the 3 option button:

  • load optimized and boot
  • load optimized default and reboot
  • enter BIOS
    Whatever I choose after restarting the computer the nightmare comes back.

What should I do? Flash the BIOS, maybe?